Descriptive Statistics: Measures of Central Tendency

Abstract

This chapter covers some basic and commonly used methods of describing your data, including calculating measures of central tendency. When we talk about measures of central tendency, we are referring to cases that fall in the middle of a distribution. In other words, we can think of these as being the typical or average case. Measures of central tendency are very efficient ways of describing how some variable is distributed in the population. It is very important in the early stages of data analysis to examine your dataset descriptively, particularly looking at the various measures of central tendency (the focus on this chapter), and dispersion (the focus of Chap. 5). Performing descriptive analyses on your data is an important part of the analysis process. Chances are, whether you are working with a dataset you have compiled or commonly available criminal justice datasets, your data will likely be a sample of some population. R makes it simple to describe your sample using the various measures of central tendency. The three common measures of central tendency reviewed in this chapter are the mean, the median, and the mode. We will demonstrate how to compute these statistics using the 2016 Body-Worn Camera Survey from the Law Enforcement Management and Administrative Statistics Survey.

Key Terms

Mean

A measure of central tendency calculated by dividing the sum of the scores by the number of cases.

Measures of central tendency

Descriptive statistics that allow us to identify the typical case in a sample or population. Measures of central tendency are measures of typicality.

Median

A measure of central tendency calculated by identifying the value or category of the score that occupies the middle position in the distribution of scores.

Mode

A measure of central tendency calculated by identifying the score or category that occurs most frequently.

Outliers

A single or small number of exceptional cases that substantially deviate from the general pattern of scores.

Tibble

Modern version of base R’s data frame (simpler and more user-friendly) that is from the tidyverse package.